For statistically homogeneous media, the one-point function is simply the volume fraction of the phase of interest, e.g., \(S_1(\mathbf {x}_1)=\phi \) , and hence position-independent. The two-point function \(S_2(\mathbf {x}_1,\mathbf {x}_2)\) , which is readily obtained from scattering experiments [1]}, [2]}, encodes information about pair separations, and only depends on the relative displacement \({\bf r}={\bf x}_2-{\bf x}_1\)  for homogeneous media. The three-point function \(S_3(\mathbf {x}_1,\mathbf {x}_2,\mathbf {x}_3)\)  contains information about how these pair separations are assembled into triangles.
